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Homework Help: My way of finding lengths between 2 pts(complex numbers),what's wrong?

  1. Mar 4, 2007 #1

    inv

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    [Solved]Length formula to find lengths between 2 pts(complex numbers),what's wrong?

    1. The problem statement, all variables and given/known data
    I've 3 pts U(2i),A(-√3 -i) & B(√3-i),all complex numbers.A question asks me to prove UAB is equilateral.


    2. Relevant equations
    |AB|=√{(b-a)^2} for finding lengths.


    3. The attempt at a solution
    So I try to find two of it's lengths AB and UA.
    |AB|=√(b-a)^2
    =√{4(3)}
    =√12
    |UA|=√{a-u}^2
    =√(-√3-3i)^2
    =√(3-9)
    =√-6
    The two lengths not same,what's wrong here?
     
    Last edited: Mar 4, 2007
  2. jcsd
  3. Mar 4, 2007 #2

    Hootenanny

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    Staff Emeritus
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    Gold Member

    In general we can find the modulus of a complex number thus;

    [tex]|z| = \sqrt{z\bar{z}}[/tex]

    Also note that [itex]\left(-\sqrt{3}-3i\right)^2 \neq (3-9)[/itex] as you have in your solution for |UA|
     
  4. Mar 4, 2007 #3

    inv

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    Problem solved and thx indeed*
     
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